Car A is travelling at a constant speed of 100mph at the time it passes a stationary vehicle (Car B). If the Car B hopes to catch Car A within a mile, how fast must Car B travel? Assume Car B can accelerate from 0-60mph in 6 seconds.
If B wants to catch A in a mile, then that means he only has 1/100 hr.
Now, if we assume that B can continue to accelerate at the same rate he did to get to 60 mph, then that makes a =60mph/6sec = 10mph/sec = 10mi/(hr*sec) = 10mi(hr*1/3600hr) = 36000mi/hr²
At this point we are stuck. If B accelerates only to 100mph or less, he'll forever be behind A.
If he accelerates to some speed > 100mph, then there are many answers, depending on just how fast he ends up going.
If he accelerates at the same rate for the whole 36 seconds, then he ends up going v = at = 36000mi/hr² * 1/100 hr = 360 mi/hr
s = 18000 * 1/10000 = 1.8mi
So, if he accelerates constantly, he goes 1.8 mi in 1/100 hr. So, he catches A in less than 36 seconds.
So, how far does A get if a constantly accelerating B comes zipping up on his way to 360mph?
100t = 18000 t²
100 = 18000 t
t = 1/180 hr = 20 seconds.
So, the fastest A can catch B is 20 seconds, in 5/9 miles, having reached a speed of 200 mph.
Depending on acceleration, any time from
20 seconds on is possible.
Would it be plausible for Car B to catch Car A within .5 mile?
So, in half the distance? No. Read above. Unless he can increase his acceleration, B cannot overtake A in less than 5/9 miles.
To determine how fast Car B must travel in order to catch up with Car A within a mile, we need to find the time it takes for Car B to reach Car A and calculate the speed required for that time.
First, let's find the time it takes for Car B to accelerate from 0-60mph. We are given that Car B can accelerate from 0-60mph in 6 seconds.
Next, we need to find the time it takes for Car A to cover a mile at a constant speed of 100mph. Using the formula for time, which is distance divided by speed, we can calculate:
Time taken by Car A to cover a mile = 1 mile / 100 mph
Now, comparing the times of Car B accelerating and Car A covering a mile, we need to ensure that Car B takes less time. If Car B takes longer than Car A to reach the same distance, it will not be able to catch up.
If Car B takes less than 1 mile divided by Car B's speed to cover the mile, it will be able to catch up with Car A.
Therefore, the speed at which Car B needs to travel can be calculated using the formula:
Speed of Car B = 1 mile / (Time taken by Car A to cover a mile - Time taken by Car B to accelerate from 0-60mph)
Let's substitute the values into the formula:
Speed of Car B = 1 mile / ((1 mile / 100 mph) - 6 seconds)
Please note that we need to convert the time taken by Car B to accelerate from seconds to hours to maintain the consistency of the units. So, 6 seconds is equal to 6/3600 hours.
Speed of Car B = 1 mile / ((1 mile / 100 mph) - (6/3600) hours)
Now, let's simplify the equation:
Speed of Car B = 1 mile / ((1/100) - (6/3600)) hours
Speed of Car B = 1 mile / (0.01 - 0.00167) hours
Speed of Car B = 1 mile / 0.00833 hours
Speed of Car B ≈ 120 mph
Therefore, Car B must travel at approximately 120 mph in order to catch up with Car A within a mile.